Discourse Activities-Improving Discourse Activities-Improving Mathematical Language Mathematical Language AcquisitionAcquisition

National Partnerships Schools’ ForumMelbourne, February 2012Michelle Bootes Euroa Secondary College

Literacy in Mathematics and Literacy in Mathematics and Mathematical LiteracyMathematical Literacy

“... literacy in mathematics, that is, how students access mathematics through language, and with the role that language plays in mathematics teaching and learning.”

[ p. 3 Meiers 2010]

Mathematical Literacy (or numeracy) Is “an individual’s capacity to identify and understand the role mathematics plays in the world ... to use and engage with mathematics in ways that meet the needs of the individual …”

[ PISA, as cited in OECD, 2004, p.15]

COAG recommended:“That the language and literacies of mathematics be explicitly taught by all teachers of mathematics …”

(National Numeracy Review Report, p34)

Literacy instruction is also a necessary part ofmathematics instruction (Draper 2002).

ProjectProjectTitle:Discourse Activities: Can They Improve

Student Mathematical Vocabulary Learning?

Research Question:What kind(s) of discourse strategies are

associated with the best improvement in the mathematical language acquisition of low-achieving Year 7 students from low-SES backgrounds?

DefinitionsDefinitions• Low-Achieving (LA) is defined as those

Year 7 students who scored below a VELS Level 4.0 in the On Demand Adaptive Number Testing in February 2011.

• “Discourse Activities” are learning activities which allow students to use dialogue and discussion as part of their learning [Zack and Graves (2001), Hufferd-Ackles, Fuson and Sherin (2004), Marino (2005), Kersaint (2007)].

MethodologyMethodology Vocabulary Pre and Post-Test (All

Year 7 students) Teacher Journal (All Year 7

teachers)

Lesson Components: Active Teaching Imagined Representations Purposeful Games and Puzzles What if? Fluency Tasks

Nicholson (1989) considered it to be of great importance to diagnose whether or not key words are available to students and are properly understood.

Discourse Activities1

1. Sullivan, P. (2011) Creating Mathematics Lessons. Retrieved from EDF6421, Monash University Studies Online: http://muso.monash.edu.au

Activity 1: Essential Activity 1: Essential VocabularyVocabulary

Nicholson (1989) considered it to be of great importance to diagnose whether or not key words are available to students and are properly understood.

Task 1: In pairs, write a list of essential key mathematical words that will be used in your next mathematics unit or topic.

Task 2: Complete the Fraction Vocab sheet. Estimate the number of students who properly understand the words in the list.

Cloze Activity Generatorhttp://worksheets.theteacherscorner.net/make-your-own/fill-in-the-blank/

Results: GroupResults: Group

Year 7 Group out of denominator

equivalent to

improper fraction

equal parts mixed number reduced to

proper fraction numerator fraction

A-pre 40 33 7 13 73 20 13 33 40 60

A-post 87 87 60 60 100 53 73 67 93 93

B-pre 83 58 92 67 100 50 92 50 83 100

B-post 83 92 83 83 100 67 83 67 83 92

C-pre 93 87 87 80 93 47 53 60 80 93

C-post 100 100 73 100 100 93 73 80 93 100

D-pre 95 95 95 90 100 65 95 65 95 100

D-post 100 100 100 100 100 95 100 95 100 100

Percentage of Students With Correct Response In Each Group

Low Achieving Students High Achieving Students Anomalies between pre and post-tests

Fraction Vocabulary

Results: Pre and Post Vocabulary Results: Pre and Post Vocabulary TestsTests

Results:Teacher Journals

LA:Groups A and B

HA: Groups C and D

ConclusionsConclusions::

1. Suggests that “Purposeful Games and Puzzles” and “Imagined Representations” may lead to the best improvement in language acquisition for the low achieving groups.

2. “Active Teaching”-Traditional with little opportunity for discourse does not improve language learning, even for high achieving students.

3. It is of “great importance to diagnose whether or not key words are available to students and are properly understood” (Nicholson, 1989), and for teachers to select discourse strategies that will improve language acquisition.

Purposeful Games and Purposeful Games and Puzzles (PGPs)Puzzles (PGPs)

PossibleLesson

Component/s

Teacher Introduction

Students Working

Teacher Review

Purposeful Games and

Puzzles

Explaining rules and demonstrating game:Relationship cardsRace to ...DIY ExperienceLoop Cards

Student playing games in mixed groups, with like needs pairs evolving.

Synthesis of student products and summary teaching.

Sullivan, P. (2011b). Creating Mathematics Lessons. Retrieved from EDF6421, Monash University Studies Online: http://muso.monash.edu.au

Mathematical Games:Mathematical Games:Race to …………… Race to …………… (Brousseau, (Brousseau, 1997)1997)

Race to 10, start at 0, adding 1 or 2.

Race to 3, start at 0, adding ½ or ¼

Race to 1, start at 0, adding 0.1, 0.05 or 0.15

Race to 0, start at 100, taking away any number from 1 to 12

Race to 5x + 5y, start at 0, adding x, y or x + y

Race to 128, start at 1, multiplying by 2, √2 , 2√2

Sullivan, P. (2011). Creating Mathematics Lessons. Retrieved from EDF6421, Monash University Studies Online: http://muso.monash.edu.au

Activity 2:Activity 2:What might a “Race to … ” task look like for your unit or topic?

Design a task and try this out on a partner.

Each game can be extended to more conventional exercises utilising the particular skill that has been practiced.

Students find it engaging to choose:The ways of workingThe type of examplesThe level of complexity.

Puzzles: Relationship Puzzles: Relationship CardsCardsThe following is an example of a mathematical puzzle, adapted from a suggestion by Swan (no date). The puzzle involves a set of term (or number) cards and operation cards (Relationship Cards), a subset of which could be:

Activity 3: In teams, use the decks provided, choose the two operation cards that can be placed between the two term cards to represent the connection.

Activity 4: Using the blank card sheet, develop another relationship puzzle.

Loop Cards:Loop Cards:

Whole Class Loopshttp://www.emu.org.uk/curriculum/projects/numeracy/pages/lpcards.html

Answer

Question

Answer

Question

Activity 5:Activity 5:

Task 1:A loop card activity- some of the cards (green) can be found on your table.

Task 2:Create your own loop card activity using the sheet provided.

Summing up Summing up Purposeful Games and Purposeful Games and

PuzzlesPuzzlesStudents have to evaluate a range of possible solutions

Self-correcting

Strategy enhances the search for mathematical connections

Focuses on conceptual understandings, strategic competence and productive dispositions

Student choice is used

Medium for prompting (by teacher) for communication

Low risk for students

Factors Influencing Student Factors Influencing Student ResponseResponse

Student Choice > Contributes to motivation

Productive Communication > There is more to discuss than the correct answer

Fosters collaboration and fun

Why is student Why is student communication so communication so important?important?

Strategies that generate discourse in the mathematics classroom give students the opportunity to explain their own mathematical thinking, and make significant contributions that can be questioned and built upon by other students.(Hufferd-Ackles, Fuson and Sherin 2004)

Discourse ActivitiesDiscourse ActivitiesSeveral articles point to the importance of “student talk” in helping students to overcome language difficulties in mathematics (Aiken 1971).

Zack and Graves (2001) found that dialogue leads to learning because the participants talk about their work, things that confuse them and how the ideas of others help or do not help them to make mathematical meaning.

Learning the literacies of mathematics can be characterised as the use of oral or written language to make sense of mathematics and to communicate, solve problems and engage in discussions and decision making (Kersaint 2007).

Purpose of Discourse Purpose of Discourse ActivitiesActivities•Provides oral language (text) practice

Students:

Compare texts

Share text

New text is formed

New language is acquired.

This is language acquisition.